The six strong panel, headed by Glasgow City Council leader Gordon Matheson, met this week to consider the six shortlisted schemes.
The winner was set to be announced at a ceremony in The Lighthouse on Friday.
It will now be next week before the judges can reconvene in the hope of agreeing which architect should be appointed to carry out the £15million Glasgow project.
Mr Matheson said: "It is disappointing but it is important we get this right. We will make a decision next week."
The other judges are David Mackay, partner with Barcelona based MBM Architects, Professor Andy McMillan, former head of the Mackintosh School of Architecture at Glasgow School of Art, David Harding, former head of environmental art at Glasgow School of Art and Geoff Ellis, director of DF Concerts.
They have been considering plans for the square from architectural firms in the UK, France and America.
The competition winner will work in partnership with the council to develop the final design.
Work on George Square is due to start within weeks and one of the first jobs will be to take down the historic statues.
They will be removed for restoration but the decision on whether or not they are returned will depend on the final design for the area.
The cenotaph will remain in place during construction work but will be kept under wraps to ensure it is not damaged.
Mr Matheson has said it is vital work on the square is finished in time for the Commonwealth Games next summer when the city will be in the world spotlight.
Among the six finalists is award-winning Glasgow-based JM Architects, whose recent work includes the restoration of Glasgow School of Art, while several firms have been involved in projects around the London 2012 Olympics.
The New York-based James Corner Field Operations is behind a 1.5 mile long park, known as the High Line, built on a section of the former elevated New York Central Railroad .
The other shortlisted firms are Agence Ter from France and Burns + Nice and John McAslan & Partners from the UK.
The designs are on display in The Lighthouse in Mitchell lane and can be seen on Glasgow City Council's website
The public can leave comments online until 5pm on Friday, January 18.
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